Single cell encoding with quantum dots as live cell optical tracers for deriving proliferation parameters has been developed using modelling to investigate cell cycle and proliferative outputs of human osteosarcoma cells undergoing mitotic bypass and endocycle routing. A computer-based simulation of the evolving cell population provides information on the dilution and segregation of nanoparticle dose cell by cell division and allows quantitative assessment of patterns of division, at both single cell and including whole population level cell cycle routing, with no a-priori knowledge of the population proliferation potential. The output therefore provides a unique mitotic distribution function that represents a convolution of cell cycle kinetics (cell division) and the partitioning coefficient for the labelled cell compartment (daughter-daughter inheritance or lineage asymmetry). The current study has shown that the cellular quantum dot fluorescence reduced over time as the particles were diluted by the process of cell division and had the properties of a non-random highly asymmetric event. Asymmetric nanoparticle segregation in the endosomal compartment has major implications on cell-fate determining signaling pathways and could lead to an understanding of the origins of unique proliferation and drug-resistance characteristics within a tumour cell lineage.